Hand-operated cutting machines with annular saw blade have great advantages over cutting machines with saw blade with traditional centre drive. The predominant advantage is that they provide an extremely large cutting depth in relation to the diameter of the blade. They, however, also have other advantages, among other a great ergonomic advantage; they are relatively light-weighted. Yet, there exists a need to improve them in ergonomic aspect. Above all, it is for this machine type, as for other cutting machines of the above kind, desirable that the operator should be able to hold and to manoeuvre the machine in a, from an ergonomic viewpoint best mode which may vary from person to person, and also in consideration of the demands that are raised in different operating situations. It is from an ergonomic viewpoint also desirable to be able to reduce the total weight of the machine still further and to distribute the mass to make the machine well balanced.